Chinese Classical Mahjong

Chinese Classical mahjong is the ancestral form, sometimes called the “old Chinese” style. It is built like any mahjong. A winning hand is four melds and one pair, made from the standard set of 144 tiles. A meld is a set of three or four matching tiles, or a run of three. What sets the classical game apart is how a finished hand is scored and paid. This is the older, fuller scoring system. Joseph Babcock introduced it to the West in the early 1920s with his Rules of Mah-Jongg (the famous “red book”), and A. D. Millington later wrote it up in The Complete Book of Mah-Jongg. The British Mah-Jong rules follow this lineage. The faster scoring of modern Hong Kong play is a streamlined descendant of it.

The defining trait is points plus doubles, capped by a limit. You first add up base points for the win itself and for each scoring element — pungs (three of a kind), kongs (four of a kind), valuable pairs, flowers and seasons. Then certain patterns each double the running total: dragon and wind triplets, a one-suit hand, a hand with no sequences, and so on. The doubled figure is then capped at an agreed limit (classically 500 points; many tables use 1,000). A few rare hands score the full limit outright.

Settlement is richer too. All three opponents pay the winner, and the dealer (East) both pays and receives double. In full classical play the three losers also settle the differences between their own hands, so even a hand that did not win can earn or owe. Hong Kong keeps the points-and-doubles skeleton but trims most of this away. That is why the two games feel related but are not identical.

How it differs from Hong Kong

The deal uses the familiar mahjong setup — all 144 tiles built into a square wall, dealt to four players, each building toward a hand of four sets plus a pair. Two parts of the setup matter more here than in faster play: the prevailing (round) wind, which feeds directly into scoring, and the loose tiles set aside to replace kongs and flowers.

The four-round game and the prevailing wind

A full game runs four rounds, each named for a prevailing wind in the fixed order East → South → West → North. Within each round every player serves at least once as dealer, so a round is at least four hands and a complete game is 16 hands or more — it stretches whenever the dealer wins or a hand washes out.

The prevailing wind affects scoring. A pung or kong of the round wind is worth one double, exactly like a pung of your own seat wind. In the Millington/British school, if your seat wind and the round wind are the same tile (you sit East in the East round), that single triplet can earn two doubles — one for seat, one for round.

Dealer and how the deal passes

1. Seat the winds. Dice (with a draw of the four wind tiles) settle who starts as East. East is the dealer; the others take South, West, and North going counter-clockwise.
2. East keeps the deal on a win — and, in the classical/British school, on a wash-out. If the dealer goes Mah-Jong, East stays East and an extra hand is played. Most classical tables also keep East on a drawn ("goulash") hand with no winner; seats do not move.
3. Otherwise the deal passes counter-clockwise. When any other player wins, the deal moves on: the player who was South becomes the new East. When the deal has cycled all the way around the table, the prevailing wind advances to the next round.

The dead wall and loose tiles

After breaking the wall, a block of tiles at the broken end is fenced off as the dead wall (the "kong box"). These are the loose tiles — the supply you draw a replacement from every time you declare a kong or expose a flower. You never draw your normal turn tile from here, and the +2 self-draw bonus is only for the winning tile taken from the live wall, not from this box.

How flowers and seasons score

In the classical game the eight flowers and seasons score points, so they are always declared face-up.

• Set out at once. Any flower or season in your dealt hand is laid face-up beside your hand immediately, and you draw a loose tile to replace it. The same happens the moment you draw one during play.
• Every bonus tile scores 4 points just for being shown.
• Match your seat number for a double. Flowers and seasons are numbered East = 1, South = 2, West = 3, North = 4. In the British and most common scoring, the flower (or season) bearing your seat's number earns one double each — and because your seat changes as the deal moves, a flower that scores a double this hand may score none next hand.
• Collecting a full set — all four flowers, or all four seasons — is worth a further double in Millington's own scoring (the British school scores a complete set as two doubles).

In Chinese Classical scoring you count base points first, then multiply by doubles. This section covers only the base points the winner adds up before any doubling. Three rules explain almost every number below. A concealed set outscores an exposed one. Terminals and honours (1s, 9s, winds and dragons) outscore the simple 2–8 tiles. And a kong scores roughly four times its matching pung.

Points for sets

A kong claimed by adding a fourth tile to an exposed pung counts as exposed; only a kong assembled wholly from the wall and your own hand counts as concealed. The exposed/concealed distinction is also why you keep a concealed kong face-down until the hand ends. You may declare it only to draw the replacement tile, and it still scores at the concealed rate.

Pairs, flowers & the win itself

• Pair of dragons — 2 points.
• Pair of your seat wind — 2 points; pair of the round (prevailing) wind — 2 points. A pair that is both your seat wind and the round wind scores 2 + 2 = 4 at most tables (some score only 2).
• Each flower or season tile — 4 points apiece. They are set aside face-up and replaced with a fresh draw the moment they appear, then scored at the end.
• Going Mah-Jong (completing the hand) — 20 points to the winner only (Millington / British / North American value; some older tables use 10).
• Ordinary pairs of simples, and a pair of a wind that is neither your seat wind nor the round wind, score nothing.

Winning bonuses

These extra base points go to the winner only, added before doubling. They are not mutually exclusive — a self-draw that is also the only fitting tile earns both +2s.

• Self-draw (winning tile taken from the wall, not a discard) — +2.
• Only-tile wait — winning on the single tile that can complete the hand: an edge wait (1–2 waiting 3, or 8–9 waiting 7), a closed/middle wait (e.g. 4–6 waiting 5), or a single-tile pair wait — +2.
• Out on a loose / supplement tile drawn to replace a tile after declaring your own kong — +2.
• Robbing a kong — winning on the tile an opponent adds to promote an exposed pung to a kong — +2.

Base points get you a running total. Doubles are the multiplier layer that sits on top of it. Where base points reward the building blocks of a hand — pungs, kongs, the pair, flowers — doubles reward shape: a one-suit hand, a hand with no sequences, or a pung of your seat wind.

Each double does exactly what the name says: it doubles your entire running total. They stack, so a hand worth two doubles is multiplied by four, three doubles by eight, four doubles by sixteen, and so on. A few doubles can take a 30-point hand to the limit.

Order of operations

Sum every base point first, then apply the doubles to that total — once each, all at the end. Do not double individual scoring items as you go.

1. Add up all base points: 20 for going Mah-Jong, plus pungs, kongs, the pair, flowers, and any winning bonuses.
2. Count how many doubles the hand earns from the table above.
3. Apply them to the total: total = points × 2^{(number of doubles)}.

So two doubles multiplies by 4, three by 8, four by 16. The doubles are applied to the whole base total at once — not item by item — which is exactly why one or two of them swing a hand so hard.

The seat-and-round wind variant

One rule worth pinning down before you sit down: a single wind can be both your seat wind and the prevailing round wind — for example, you are sitting East in the East round. Most classical tables, including the British Mah-Jong rules, let a pung of that wind score 2 doubles: one for the seat, one for the round. A minority of rule sets count it only once. Agree which before play, because it routinely decides whether a hand reaches the limit.

In Chinese Classical scoring, a single hand is worth its base points multiplied by two for every double it earns — the running total is points × 2^doubles. These totals grow fast: a full flush with several dragon pungs can run into the thousands. To keep settlement sane, the table agrees in advance on a limit — the most any one hand can ever pay out. Any hand whose score meets or exceeds the limit simply scores the limit, and no further.

Limit hands

Separately, a handful of rare patterns are so prized that they pay the full limit outright, regardless of how few points they would otherwise count. These are the limit hands. Unless noted, each is still a normal four-sets-plus-a-pair hand; several are required to be concealed.

A note on the two trickiest. Thirteen Orphans is one of every terminal and honour — the 1 and 9 of each suit, each of the four winds, and each of the three dragons — with one of those tiles duplicated to make the pair. Nine Gates is a single suit holding three 1s, three 9s, and one each of 2 through 8, won on any further tile of that suit.

A few related patterns sit just below the top tier. Little Three Dragons (two dragon pungs + a pair of the third) is a strong doubling hand but not a limit hand. And some British-style rule sets score certain hands as a half-limit (250 of a 500 limit) rather than the full amount — Earthly Hand is the standard example in Millington, and some tables also half-score a plain one-suit flush (Purity / 清一色) or other near-misses.

Classical settlement differs from faster games in three ways: everyone pays the winner, the dealer's payments and receipts are both doubled, and in the fullest version the losers also settle with each other. This three-part settlement is the main thing modern Hong Kong play dropped.

The core rule: all three losers pay the winner

When a player goes Mah-Jong, each of the other three players pays the winner the full value of the winning hand — not a split, not a share. If the hand is worth 40 points, the winner collects 40 from each loser, for 120 in total. In casual play, often only the discarder pays. (The winner always takes the round, even if a loser's own hand happened to score more.)

The dealer (East) doubles — both directions

Every payment to or from East is doubled:

• If a non-dealer wins: the two non-dealer losers each pay the hand's full value, but East pays double that value.
• If the dealer (East) wins: every loser pays double the hand's value, so East's winning hands pay out twice as much.
• The doubling also applies to the loser-to-loser settlement below: any difference paid to or from East is doubled.

The fuller method: losers settle with each other

Traditional Classical settlement does not stop at paying the winner. Each of the three losers also scores their own (unfinished) hand — counting their pungs, kongs, flowers, doubles, and so on, but omitting the 20 for going out and the win-only bonuses, since they did not win. Then every pair of losers exchanges the difference of their two totals: the lower hand pays the higher hand the gap between them, with East's share doubled as always.

This rewards building a strong hand even when you do not win, and it is the historically correct method (Millington's rules call it out as the full Classical procedure). Many modern tables drop it and pay only the winner — both are in common use, so agree before you start.

Discarder Responsibility — Pao (包)

For the largest limit hands, fuller classical (and Chinese Official) rules add a penalty for feeding the killing tile. Under Pao (包, "liability"), if an opponent has already exposed two dragon pungs/kongs and you discard the third dragon to complete Big Three Dragons (大三元) — or has three wind pungs exposed and you feed the fourth wind for Big Four Winds (大四喜) — you alone pay the entire limit for all three losers. The other two pay nothing. The reason: with the giant hand already exposed, the player who supplies the final tile takes responsibility for it.

The trigger is that the big hand must have been visible (its other dragons or winds already melded face-up) at the moment you discarded; a Pao hand completed by self-draw, or one assembled concealed, is settled normally. Plenty of casual Classical tables omit Pao entirely.

And all of it is bounded: the limit caps the value of any single hand (classically 500 points; many tables use 1,000, and some English clubs 2,000) before payment. The cap is applied to the hand first, then the East doubling is layered on top — so a dealer can still collect up to twice the limit from each loser.

Most of your score comes from doubles, not base points. A double multiplies your whole total. A point adds a little. Two extra simple pungs add four points. One flush multiplies everything by four. Before any move, ask whether it earns another double or only adds points. Build toward doubles, stay concealed long enough to keep the concealed-hand double, and watch the table for the limit hands that can make you pay alone. (A pung is three of a kind; a chow is a run of three in one suit; a double multiplies your whole total by 2.)

What to build: aim for doubles

Commit to one suit early. A full flush is three doubles (×8); a half-flush is one (×2). If by your sixth or seventh draw you hold 7+ tiles of one suit plus honours, discard your weakest off-suit tile and go for the full flush. Settling for a half-flush to keep a stray chow suit costs you a ×4 jump. Then add more doubles on top of it:

• Pung the right honours, never chow. A chow is 0 points and 0 doubles. A dragon, seat-wind, or round-wind pung is points plus a double each, and using no chows at all earns the all-pungs double too. (A guest-wind pung — a wind that is neither your seat nor the round — pays points but no double, so it helps only through all-pungs or the flush.) Three scoring honour pungs can add 3–4 doubles before the flush even counts.
• Treat your own flower or season as a double, not a bonus. Your own flower is 4 points and a ×2; an off-seat flower is just the 4 points, no double. Once you hold one own-flower double, the cheapest way to the cap is one more double, not another pung for base points.
• When two dragons are paired, take the third over anything. Two dragon pungs plus the third dragon as a pair is already about 3 doubles (two pung doubles plus little three dragons). Completing that pair into the third pung gives you Big Three Dragons, which pays the limit outright.

Speed vs value: stay concealed, and don't claim to hurry

The fully-concealed double is a ×2 on the entire hand. It doubles your base points and every other double you already hold. A flat 30-point open hand is 60 concealed; a hand at ×4 becomes ×8 just by staying closed. That math is why the small tempo loss of passing on a discard is almost always worth it. (A concealed set is one you build in hand; an exposed set is one you claim from a discard, and claiming it ends your fully-concealed double.)

• Don't claim a pung you already hold two of. Claiming the discard halves that triplet's base points (exposed 2 vs concealed 4 for simples; 4 vs 8 for terminals and honours) and locks your hand open, which kills the concealed double on everything. Only claim if it wins the hand outright.
• Hold concealed kongs; don't kong off a discard. A concealed kong is double the base of an exposed one (simples 16 vs 8; terminals and honours 32 vs 16) and keeps your hand concealed. Drawing the fourth tile to declare a concealed kong — and taking the replacement draw — is fine. Exposing a meld to kong someone's discard for the base bump is a bad trade.
• Aim your final wait toward self-draw. Self-draw is +2 points and keeps the hand off the table, which secures the fully-concealed double. Being fed an honour to complete a pung forces you to meld it exposed (base 4 instead of 8) and breaks concealment. So prefer the wait you are more likely to draw than be handed.

Defence: watch for limit hands, and East pays and collects double

One-suit hands often grow to ×8 and beyond and hit the limit. The moment a player is clearly collecting a single suit plus honours, give up the hand: discard off-suit tiles and honours you already hold a pair of, and concede the small loss. The biggest risk is Pao. Feeding the completing tile of Big Three Dragons or Big Four Winds makes you alone pay the whole limit instead of splitting it three ways.

• Read exposed melds before every risky discard. Visible dragon and wind pungs and kongs show you the doubles already locked in. Two dragon pungs down means you never release the third dragon. Hold every copy to the end. The same goes for a third wind once two wind pungs show.
• Block the dealer first. East pays and collects at double the settlement, so the same hand costs you about 2× more. When you can only stop one threat, stop East's. When you must deal in, prefer a non-dealer's modest hand.
• If you can't win, don't finish poorest. Losers also settle the differences between their hands, so a bare 20-point hand pays out to everyone above it. Late in the hand, give up the full-flush plan and grab cheap honour pairs and a flower so your hand isn't the table's lowest.

Where the value is, and when to stop

Doubles compound, so the jumps that matter aren't evenly spaced. The table below shows where the big steps are. Once your points × multiplier already clears the cap, stop optimizing and go out. Extra flowers, self-draw, and the only-tile-wait add nothing past the limit, and over-reaching just risks the hand to an opponent who then pays you zero. Also, don't give up a winning flowered double-stack to chase a named limit hand. The limit is a flat ceiling that flowers and points can't raise, and the named hand is usually far less likely to complete.

If you're East, weight all of this even more heavily. Your deal pays and collects at double the table's settlement, so the dealer seat is the one to over-invest in doubles and never waste on a cheap, fast, double-poor win.

Two layers of mathematics sit under the game. The first is the draw, and it works the same in every style of mahjong. At any moment, some number u of tiles are unknown to you. Your hand is waiting on w of them. Each unknown tile you turn over wins for you with probability w/u (the tiles are sampled without replacement). The width of your wait matters. A fully-live two-sided wait, say 4-5 needing a 3 or 6, has w = 8 winning tiles, about 8% a draw. A closed wait has only 4 winning tiles. The widest legal wait of all is the Nine Gates (1112345678999, which completes on any of the nine ranks) and waits on 23 tiles. The second layer is the payoff. Chinese Classical scores its payoff differently from other styles.

Value is multiplicative

Score is (sum of base points) × 2^doubles. You take the base total and double it once for every “double” the hand earns. Two doubles quadruple it. Three doubles multiply it by eight, and so on. 2^doubles means 2 multiplied by itself that many times. A point adds to the total. A double multiplies the total. Two extra simple pungs (a pung is a set of three identical tiles) add +4 points. A single flush adds ×4 on the entire pile. So a hand’s value depends almost entirely on its number of doubles, not its base points. A full flush (3 doubles, ×8) is worth more than any amount of patient pung-stacking you could realistically assemble.

Heavy tails, the limit, and variance

Because value scales as 2^doubles, the score distribution is right-skewed and log-scaled. The typical (median) hand is worth less than the average. The average is pulled up by the rare high-double hands. The classical limit (500 points, often 1,000) caps the multiplicative payoff. It cuts off the tail of that distribution. Once the limit applies, the gap between the largest and smallest hands stays finite and moderate. The large mean-versus-median separation is a property of the distribution before the cap. The consequence for play: chasing doubles has positive expected value but high variance. So hand selection is a bankroll question (the Kelly criterion) rather than a pure expected-value one. Go for the big hand when you can afford the swings, and take the sure small one when you cannot.

A simple model shows why the cap matters for risk, not only for size. Suppose each extra double is about a fraction q as likely as the one before, so the number of doubles falls off geometrically. The mean multiplier E[2^doubles] is then finite only when doubles thin out faster than half each step (q < 1/2). The variance depends on E[4^doubles], which needs the stricter condition q < 1/4. A hand distribution can therefore have a finite average value and still have infinite variance. Take q = 0.4: the average hand is worth about ×3 its base points, but the variance is infinite, because rare large hands dominate the spread. Cap the doubles at five and the average barely moves, to about ×2.3, while the standard deviation becomes finite, about ×3.8. The limit changes the average payout very little. Its main effect is to make the swings finite, which keeps the game playable.

Pao: variance, concentrated

The pao (包) rule applies when you feed the tile that completes a Big Three Dragons or Big Four Winds. You alone then pay the whole limit. Under pao, one player pays the game’s largest payout alone instead of sharing it, which is the worst single outcome a loser can face. In classical defence, never discard the tile that completes an opponent’s third dragon or fourth wind once the rest of that set is exposed.